Broadband CARS Spectral Phase Retrieval Using a Time-Domain Kramers-Kronig Transform

Published

April 22, 2009

Author(s)

Yuexin Liu, Young Jong Lee, Marcus T. Cicerone

Abstract

We describe a closed-form approach for performing a Kramers-Kronig (KK) transform on data of finite frequency range; the method is analytically exact and computationally simple and robust. In this approach we transform the frequency domain data to the time domain, perform an operation that ensures a causality criterion is met, then transform back to the frequency domain. We demonstrate that this approach is equivalent to a KK transform, and can be used to rapidly and reliably retrieve the phase, and thus the resonant component, from a broadband coherent anti-Stokes Raman scattering (CARS) spectrum. The fact that this method handles causality in the time domain allows us to account for spectrally varying nonresonant background (NRB) from CARS in a natural way, as a response function with a finite rise-time. This method also eliminates many of the difficulties typically encountered in applying KK transforms, including the need to use numerical integration and the consideration of Cauchy principal parts for dealing with infinities.

Citation

Optics Letters

Volume

34

Issue

9

Pub Type

Journals

Download Paper

https://doi.org/10.1364/OL.34.001363

Local Download

Keywords

Kramers-Kronig relations, spectroscopy, coherent anti-Stokes Raman scattering, phase retrieval

Citation

Liu, Y. , Lee, Y. and Cicerone, M. (2009), Broadband CARS Spectral Phase Retrieval Using a Time-Domain Kramers-Kronig Transform, Optics Letters, [online], https://doi.org/10.1364/OL.34.001363, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=901217 (Accessed December 22, 2024)